Chapter 3, Problem 1CE

To determine

A function $f\left(x\right)$ describing a parabolic arch.

Answer to Problem 1CE

Solution:

The parabolic arch is described by $f\left(x\right)=\frac{-20x^2}{49}+20$.

Explanation of Solution

Given:

The parabolic arch is $20$ feet tall and $14$ feet wide at base.

Explanation:

For a function whose graph is the shape of the parabolic arch is:

$f\left(x\right)=\frac{-k}{c^2}{x}^2+k$

Here $‘k’$ depicts the value of height which is $20$ and $‘c’$ represents half the value of base which is $7$. Thus,

$\begin{array}{ccc}\hfill f\left(x\right)& =& \frac{-20}{{\left(7\right)}^2}{x}^2+20\hfill \\ \hfill & =& \frac{-20}{49}{x}^2+20\hfill \end{array}$